Solve y^prime=c^x^2+1-x^3

$$y ^ { \prime } = c ^ { x ^ { 2 + 1 } } - x ^ { 3 }$$

Solve for c (complex solution)

$$c=e^{\frac{Im(x^{3})arg(x^{3})+iRe(x^{3})arg(x^{3})}{\left(\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}\right)^{3}}-\frac{2\pi n_{1}iRe(x^{3})}{\left(\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}\right)^{3}}-\frac{2\pi n_{1}Im(x^{3})}{\left(\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}\right)^{3}}}\left(|x|\right)^{\frac{3\left(Re(x^{3})-iIm(x^{3})\right)}{\left(\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}\right)^{3}}}$$

$$n_{1}\in \mathrm{Z}$$

Solve for c

$$\left\{\begin{matrix}c=\left(x^{3}\right)^{\frac{1}{x^{3}}}\text{, }&\left(Denominator(\frac{1}{x^{3}})\text{bmod}2=1\text{ and }x<0\text{ and }Numerator(x^{3})\text{bmod}2=1\text{ and }Denominator(x^{3})\text{bmod}2=1\right)\text{ or }\left(\left(x^{3}\right)^{\frac{1}{x^{3}}}<0\text{ and }x>0\text{ and }Denominator(x^{3})\text{bmod}2=1\right)\text{ or }\left(\left(x^{3}\right)^{\frac{1}{x^{3}}}>0\text{ and }x>0\right)\\c=-\left(x^{3}\right)^{\frac{1}{x^{3}}}\text{, }&\left(Denominator(\frac{1}{x^{3}})\text{bmod}2=1\text{ and }x<0\text{ and }Numerator(x^{3})\text{bmod}2=0\text{ and }Numerator(x^{3})\text{bmod}2=1\text{ and }Denominator(x^{3})\text{bmod}2=1\right)\text{ or }\left(x>0\text{ and }\left(x^{3}\right)^{\frac{1}{x^{3}}}>0\text{ and }Numerator(x^{3})\text{bmod}2=0\text{ and }Denominator(x^{3})\text{bmod}2=1\right)\text{ or }\left(x>0\text{ and }\left(x^{3}\right)^{\frac{1}{x^{3}}}<0\text{ and }Numerator(x^{3})\text{bmod}2=0\right)\end{matrix}\right.$$